Teachers at the start of the career in the North East, Yorkshire and the Humber, and more disadvantaged areas of the country will receive £2,000 in a government attempt to solve shortages.
But unions say the plans do not go far enough to address the recruitment and retention crisis, claiming the cash incentives for some will not address issues with pay, workload and funding.
Only teachers in these shortage subjects, who work in certain areas of the country, will be eligible for the extra money on top of existing bursaries during their first five years in their career.
The pilot comes after the education secretary unveiled plans earlier this year to give some new teachers extra payments as part of the government’s strategy to recruit and retain school staff.
Kevin Courtney, joint general secretary of the National Education Union, accused the education secretary of avoiding “a root and branch solution to the recruitment and retention crisis.”
He added that the announcement only focuses on some areas of the country, which means that the "overall shortages will impact more heavily on other areas".
Mr Courtney said: “Damian Hinds continues to fiddle at the edges while the real causes are in plain sight. There are systemic issues of pay, workload and funding which must be addressed both urgently and comprehensively if we are to get anywhere close to resolving teacher shortages in a sustained way.”
Geoff Barton, general secretary of the Association of School and College Leaders, said he was “pleased to see the government taking positive action.”
But he added: “We do need to be careful that further differentiating financial incentives for certain subjects does not end up impacting on the morale of other teachers.
“What the government really needs to do is to fully fund an improvement in the general level of teacher pay to aid recruitment and retention in all subjects.”
Teachers in the government’s 12 opportunity areas - which are social mobility “cold spots” where the DfE is targeting resources - can get the incentives, as can those in Yorkshire and Humber and the North East.
The move comes after a study last year revealed that A-level maths pupils in the most disadvantaged schools are almost twice as likely to have an inexperienced teacher as their counterparts in the least disadvantaged schools.
Mike Parker, director of Schools North East, a school-led network, said: “There are many factors that account for the disparity in outcomes for pupils in economically disadvantaged areas when compared with more affluent ones, but the availability and retention of teaching talent is among the greatest.
"Investing in recruitment and retention of teachers is essential not only to the future success of pupils in this area but also to the long-term economic outlook of the region."
Nick Gibb, minister for school standards, said: “Teaching remains a popular career, but we want to make sure that we can continue to attract and keep the brightest and best graduates, particularly in subjects where specialist knowledge and expertise are vital to the future success of the economy.
“The number of young people studying science and maths subjects has increased since 2010 and we have today pledged £10m investment to ensure teaching remains an attractive and fulfilling proposition and that every child has the opportunity to fulfil their potential.”